The safety and performance of gun barrels, i.e. thick-walled cylindrical geometries, can be easily compromised by defects, such as quench cracks are an issue during manufacture, trauma cracks that occur due to rough handling, and stress cracks that develop under the forces related to firing, as well as, under the environmental conditions of, and handling in, the field. Currently, typical military practice is visual and magnetic particle inspection to identify cracks during manufacture and only visual inspection once the gun is fielded. However, visual inspections will not disclose insipient cracks internal to the barrel material and proposed automated systems that scan the inside diameter of gun barrels—in both manufacture and in the field—are complex, bulky, expensive, and relatively slow.
Various dynamic methods are known for identifying and quantifying structural damage, such as stress cracks, as a change in fundamental resonant frequencies occur due to such a defect in a solid structure. The change in frequencies can often be used to detect and locate the defect, even in the presence of ambient noise. A significant amount of work in the field relates to one dimensional problems, dealing with cracked beams under axial and transverse vibration—due to the ease of modeling a real beam or rod and thereby simplifying the analysis. Particular examples of such work including a simple theory of cracked beam under axial and transverse vibrations, presented by Y. Narkis, Journal of Sound and Vibration 172(4), 549-558 (1994). Other work by P. F. Rizos et al., Journal of Sound and Vibration 138, 381-388, 475-488 (1990) and A. D. Dimarogonas, Engineering Fracture Mechanics 55(5), 831-857 (1996), also disclose such methods and review the field of crack detection using frequency spectra. Mathematical models are developed that simulate a crack as a linear spring for axial motion and as a torsion spring under transverse motion. The compliance of these springs is represented by the stress intensity factor based upon disclosures by G R Irwin, et al., Fundamental Aspect of Crack Growth and Fracture, Fracture. An Advanced Treatise, Vol. III. Engineering Fundamentals and Environmental Effects, edited by H. Liebowitz, Academic Press, New York, 1971, pp. 2-46. In all of these papers, it is shown that the natural frequencies of cracked rods and beams shift to lower values under axial or transverse loads because of the increased compliance.
A particular dynamic method was disclosed by A. Morassi, in a paper titled: Identification of a Crack in a Rod Based On Changes in a Pair of Natural Frequencies, Journal of Sound and Vibration, 242(4), 577-596 (2001), wherein a series of calculations and experiments were presented with a hypothesis expecting more reliable results, when the damage being identified was less severe and lower order frequencies were considered. Morassi concluded that his analytical model, with these factors of less damage and lower frequencies, proved extremely accurate—the percentage discrepancy between the measured and analytical values of the involved natural frequencies being lower than 1% within the 30th vibrating mode. Morassi's method included a series of experiments using an impulse force hammer to excite a steel rod of square solid cross-section to detect notches of increasing depth (damage)—the rod suspended by two steel wire ropes to simulate free-free boundary conditions, with the axial response measured by a piezoelectric accelerometer fixed in the center of an end cross-section of the rod. The vibration signals were acquired by a dynamic analyzer and then determined in the frequency domain to measure the relevant frequency response term (inertance)—using methodology detailed in a 1997 article by A. Morassi, in Inverse Problems in Engineering, 4, 231-254, titled “A Uniqueness Result on Crack Location in Vibrating Rods”.
An alternative dynamic method using impact-acoustic resonance, including Impulse Resonance Acoustic Spectroscopy (IRAS), was detailed by A. Sutin, in a presentation at the 35th Annual Review of Progress in Quantitative Nondestructive Evaluation, Chicago, Ill., 2008—the presentation titled: “Application of Impulse Resonant Acoustic Spectroscopy (IRAS) for Crack Detection in Pipes”. In IRAS, a laser vibrometer is used to detect the vibration of the specimen's surface using a laser vibrometer. The spectra of the received laser signal is analyzed using FFT, to transform the signal to the frequency spectrum, such that the narrow frequency band about the specimens' resonance frequency can be filtered and isolated, and the envelope function of that filtered signal established—which will indicate a clear splitting of the resonance frequency envelope in the presence of a crack. This methodology has been demonstrated on thin walled solid geometries, such as casing pipes, and obviously involves significant expense.
Thus there is a need in the art for a relatively low cost, simple and relatively fast method of determining the presence and location of cracks in thick walled cylindrical geometries—as it has been surprisingly found that (1) the simple one dimensional model of a cracked geometry does not apply to cylindrical geometries, (2) that some fundamental frequencies may not be affected by a crack because of its orientation.